2 research outputs found
Monte-Carlo Simulations of the First Passage Time for Multivariate Jump-Diffusion Processes in Financial Applications
Many problems in finance require the information on the first passage time
(FPT) of a stochastic process. Mathematically, such problems are often reduced
to the evaluation of the probability density of the time for such a process to
cross a certain level, a boundary, or to enter a certain region. While in other
areas of applications the FPT problem can often be solved analytically, in
finance we usually have to resort to the application of numerical procedures,
in particular when we deal with jump-diffusion stochastic processes (JDP). In
this paper, we propose a Monte-Carlo-based methodology for the solution of the
first passage time problem in the context of multivariate (and correlated)
jump-diffusion processes. The developed technique provide an efficient tool for
a number of applications, including credit risk and option pricing. We
demonstrate its applicability to the analysis of the default rates and default
correlations of several different, but correlated firms via a set of empirical
data.Comment: Keywords: First passage time; Monte Carlo simulation; Multivariate
jump-diffusion processes; Credit ris
Solving Stochastic Differential Equations with Jump-Diffusion Efficiently: Applications to FPT Problems in Credit Risk
The first passage time (FPT) problem is ubiquitous in many applications. In
finance, we often have to deal with stochastic processes with jump-diffusion,
so that the FTP problem is reducible to a stochastic differential equation with
jump-diffusion. While the application of the conventional Monte-Carlo procedure
is possible for the solution of the resulting model, it becomes computationally
inefficient which severely restricts its applicability in many practically
interesting cases. In this contribution, we focus on the development of
efficient Monte-Carlo-based computational procedures for solving the FPT
problem under the multivariate (and correlated) jump-diffusion processes. We
also discuss the implementation of the developed Monte-Carlo-based technique
for multivariate jump-diffusion processes driving by several compound Poisson
shocks. Finally, we demonstrate the application of the developed methodologies
for analyzing the default rates and default correlations of differently rated
firms via historical data.Comment: Keywords: Default Correlation, First Passage Time, Multivariate
Jump-Diffusion Processes, Monte-Carlo Simulation, Multivariate Uniform
Sampling Metho